A target can be tracked by means of a radar of the monopulse type with great accuracy in the majority of cases where the altitude of the target is such that it allows the effects of the ground or the surface of the sea to be avoided.
However, when a target is maneuvering at very low elevation, for example less than the width of the lobe of the antenna, the antenna receives not only energy returned directly by the target but also energy which is returned by the target after reflection from the ground or the surface of the sea when the latter is smooth (specular reflection), and also the energy which is returned by the target after multiple reflections in cases where the sea is relatively rough (diffuse reflection).
In such cases, conventional processing of the sum and difference information which the radar supplies gives erroneous results. In fact, under favorable tracking conditions, in a monopulse radar the vector representing the difference signal is either in phase or in phase opposition with the vector representing the sum signal. When there is specular or diffuse reflection in the case of targets maneuvering at very low elevation, the presence of images of the target completely alters the signal received by the radar and the radar is then no longer capable of tracking properly.
Studies made of this problem have revealed that the angle formed by the sighting axis of the radar with the direction of the target, or the angular aiming error, which equals but for a proportionality factor the ratio between the values of the difference signal and the sum signal, is no longer a real quantity but a complex one. In other words, the difference signal which must be considered is no longer colinear with the sum signal but forms a certain angle with it. The result is that the difference signal contains a component colinear with the sum signal which forms its real part, and a perpendicular component which forms its imaginary part.
The same studies have also revealed that to obtain correct information on the elevation, i.e., altitude, of the target under these conditions it is necessary to take into account both these components, incorrect results being produced if altitude is assessed on the basis of the real component alone. A method of determining the altitude of a target maneuvering at low elevation using a monopulse radar has been described in an article entitled "Complex Indicated Angles Applied to Unresolved Radar Targets and Multipath" by S. M. Shermann which appeared on pages 160 to 170 of the publication IEEE Transactions on Aerospace and Electronics Systems, vol. AES 7, No 1 of January 1971.
In the case of a target where there is only a single image, it is conventionally assumed that the sum channel gives two values S.sub.A and S.sub.B corresponding to the echoes of the target A and its image B, respectively, and that the sum signal S is the resultant of signals S.sub.A and S.sub.B, i.e., S=S.sub.A +S.sub.B, A and B being the angular aiming errors for the target and its image.
The resultant difference signal D is also the vector sum of the signals D.sub.A and D.sub.B which correspond respectively to the echoes of the target and its image on the elevation difference channel. Only elevation is considered since the determination of azimuth presents no problem in the case concerned. It can therefore also be said that D=D.sub.A +D.sub.B =K(AS.sub.A +BS.sub.B), K being a proportionality factor, by analogy with the expression which for a conventionally operating monopulse radar, gives the angular aiming error for the target in relation to the sighting axis of the radar.
It can therefore be said that ##EQU1## where g is the ratio between the antenna gains in the direction of the echo of the target and in the direction of its image, r is the absolute value of the coefficient of reflection of the reflected wave, and p is the phase shift between the two echoes received by the radar. The value I/K.D/S then becomes a complex number ##EQU2## where A and B are the angular aiming errors defined above.
For an isolated target, the function (1) is real (g=o) and represents the angular aiming error A. In the case of a target accompanied by an image, this function is complex and is termed a complex angle.
If it is assumed that over a short period the quantities A and B are virtually constant, the product g.r is constant and if on the other hand the phase shift between the corresponding echoes from the target and its image varies to a sufficient degree, it can be shown that the end of the vector representing the function (1) describes a circle belonging to a family of circles which pass through the points formed by the ends of the real vectors having the values A and B. Thus, each value of the product g.r corresponds to one of the circles in the family. A second family of circles orthogonal to the first is obtained when g.r varies and .phi. remains constant, these circles passing through the points defined above.
The conventional method thus consists in determining the value of the product g.r and then, for the known value of g.r, correlating the change in the complex angle with curves which represent the possible changes over time in the values of angles A and B for a series of trajectories.
A more sophisticated method uses different frequencies or possibly times to determine three points on a circle which corresponds to a constant value of g.r. It thus becomes possible to calculate the value of the angle A. However, both these methods have a number of drawbacks. Firstly, there is still a certain amount of ambiguity due to the large number of possible intersections with the curve corresponding to each of the possible trajectories, which is generally a spiral. The number of intersections and thus of ambiguities rises sharply with the transmission frequency and the height of the radar above the sea. The result is that it is impossible to use such a method in the K.sub.u and K.sub.a bands, for example. Secondly, these methods require the product g.r to be known with accuracy.
Broadly speaking, the methods described above are complex and the noise of the receiver has a disadvantageous influence on measurement errors. It has also been found that the accuracy of the measurements becomes very much worse in the presence of diffuse reflections, even of a relatively low level. In addition, the methods described above are valid only in the field where monopulse deviation measurement is linear, owing to the structure of the function (1) involved.